Answer:
It would take 12 hours for his associate to do the complete work alone.
Step-by-step explanation:
Let 'x' be the hours taken by his associate working alone.
Given:
Time to paint the office by Dave is 4 hours.
Time to paint the office together is 3 hours.
Therefore, the part of work completed by Dave alone in 1 hour is [tex]\frac{1}{4}[/tex]
Part of work completed by an associate in 1 hour is [tex]\frac{1}{x}[/tex]
Now part of work completed by both in 1 hour is [tex]\frac{1}{3}[/tex]
Therefore,
[tex]\frac{1}{4}+\frac{1}{x}=\frac{1}{3}\\\\\frac{1}{x}=\frac{1}{3}-\frac{1}{4}\\\\\frac{1}{x}=\frac{4-3}{12}\\\\\frac{1}{x}=\frac{1}{12}\\\\x=12\ h[/tex]
Therefore, it would take 12 hours for his associate to do the complete work alone.
